A269485 Least k > 0 such that n! + k^2 is prime.

1, 1, 1, 1, 7, 11, 7, 13, 17, 31, 13, 1, 47, 17, 19, 19, 23, 73, 43, 29, 47, 31, 43, 29, 31, 37, 167, 1, 29, 43, 79, 229, 89, 71, 137, 37, 53, 1, 79, 131, 137, 1, 71, 83, 89, 89, 53, 97, 53, 101, 59, 173, 79, 71, 353, 191, 103, 523, 229, 191, 103, 401, 67, 257

Offset: 0

Author

Jean-Marc Rebert, Feb 28 2016

Keywords

• nonn

Comments

a(n) = A033932(n) = 1 for n in A002981.

Examples

			a(4) = 7, because 4! + 7^2 = 73 is prime and for 0 < i < 7, 4! + i^2 is not prime.
		

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A002981, A033932, A038202.

Programs

Mathematica

Table[SelectFirst[Range@ 10000, PrimeQ[n! + #^2] &], {n, 120}]
(* Version 10, or *)
Table[k = 1; While[! PrimeQ[n! + k^2], k++]; k, {n, 120}] (* Michael De Vlieger, Feb 28 2016 *)

PARI

a(n) = {my(k=1); while (!isprime(n! + k^2), k++); k;} \\ Michel Marcus, Feb 29 2016